Sheet gripper systems of the kind indicated are generally known in printing machines. They pull the sheet past the ink transfer cylinder during printing, and in so doing take the tension forces acting on the sheet. Since it is not possible to vary the number and spacing of the individual grippers, because of other design considerations, the tensile forces at the gripper clamping point may reach the limits of tensile sheet loading, particularly in the case of thinner materials for printing. This, of course, has an adverse effect on the quality of the print and the possible printing speed. For example, in offset printing, ink may be re-transferred from the paper surface to the blanket cylinder of a subsequent printing unit; this results in mackling if the re-transferred ink is not transferred in correct register as a result of dimensional variations due to the clamping conditions.